y^{''}-7y^'-8y=8x^2-2x

Lösung

y^{^{''}} - 7 y^{^{'}} - 8 y = 8 x^{2} - 2 x

y = c_{1} e^{8 x} + c_{2} e^{- x} - x^{2} + 2 x - 2

Schritte zur Lösung

y^{''} (x) - 7 y^{'} (x) - 8 y = 8 x^{2} - 2 x

Solve linear ODE:

y = c_{1} e^{8 x} + c_{2} e^{- x} - x^{2} + 2 x - 2

y = c_{1} e^{8 x} + c_{2} e^{- x} - x^{2} + 2 x - 2

y^{^{''}} + 16 y = cos (4 t), y (0) = 3, y^{^{'}} (0) = 2

3 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 25 y = cos (2 x)

(D^{2} + 4 D + 5) y = e^{(- x)} + 15 x

y^{^{''}} + y = 2 cos (x), y^{^{'}} (π) = 0, y (0) = 0

(D^{2} + 1) y = cos^{2} (x)